Question

In this diagram, the potential difference between $A$ and $B$ is $60V$. The potential difference across $6\mu F$ capacitor is _______ $V$.

• A. $10$
• B. $5$
• C. $20$
• D. $4$

Answer 1

Answer: (A)

$10$

The two $3\mu F$ capacitors in parallel can be combined into a single capacitor ($C$) with an equivalent capacitance of $C=3+3=6\mu F$

Now, the remaining two $3\mu F$ capacitors are in series with $C$. This can be also combined in a single capacitor of capacitance $C^{\prime }$.

$\frac{1}{C^{\prime }}=\frac{1}{3}+\frac{1}{3}+\frac{1}{6}$

$C^{\prime }=\frac{6}{5}\mu F$

Now, in series charge across all the capacitors is same and voltage add up to give the equivalent voltage.

Let required voltage across the $6\mu F$ capacitor be $V$ and the voltage across $C^{\prime }$ be $V^{\prime }$

Let charge across each of the two capacitors be $Q$

Using definition of capacitance and same charge,

$Q=Q$

$6V=\frac{6}{5}{V}^{\prime }$

Given $V+V^{\prime }=60$

Solving above two equations, $V=10V$